Alphabetize my Dvd's

[BMAD]

My DVD Shelves used to be organized by genre and frequency of watching. Now that I spend less time watching DVDs I find myself desiring to arrange these DVDs in alphabetical order. I don't care if they are left to right OR right to left, i am not that picky. To arrange my DVDs with precision I will take one DVD off the shelf and place it in the correct spot back on the shelf. If I have 11 DVDs what is the most moves I can expect to make? What if I had two shelves of 11 DVDs each?

[nana77]

for 11

Spoiler

per Erdos, at least 4 are already in order, so at most 7 dvd's must be moved to their correct locations.

for 22 on one shelf

Spoiler

per Erdos, at least 6 are already in order, so at most 16 dvd's must be moved to their correct locations.

for 22 on 2 shelves

Spoiler

Since shelf order does not matter, worst case scenario is each shelf has 6 dvds which will remain on the shelf and 5 it will trade with the other shelf. Any dvd leaving one shelf will have a counterpart on the other shelf that needs to change shelves as well. Of the 6 that remain on the shelf, worst case is 2 will be in order. So 4 dvd's total are in order and on the correct shelf, meaning the other 18 dvd's must move.